Qualitative properties of solutions to a nonlinear transmission problem for an elastic Bresse beam - Fastovska, Tamara; Langemann, Dirk; Ryzhkova, Iryna (Frontiers in Applied Mathematics and Statistics, 2024)
We consider a nonlinear transmission problem for a Bresse beam, which consists of two parts, damped and undamped. The mechanical damping in the damped part is present in the shear angle equation only, and the damped part may be of arbitrary positive length. We prove wellposedness of the corresponding system in energy space and establish existence of a regular global attractor under certain conditions on nonlinearities and coefficients of the damped part only. Besides we study singular limits of the problem under consideration when curvature tends to zero or curvature tends to zero and simultaneously shear moduli tend to infinity, and perform numerical modelling for these processes.